1. No Clickers
Bellwork
State which postulate justifies each statement
If D is in the interior of ABC, then mABD+ mDBC=mABC
If M is between X and Y, then XM+MY=XY
Find the measure of MN if N is between M and P and MP=6x-2, MN=4x, and MP=16.

2. Bellwork Solution State which postulate justifies each statement
If D is in the interior of ABC, then mABD+ mDBC=mABC
Angle Addition Postulate

3. Bellwork Solution If M is between X and Y, then XM+MY=XY
State which postulate justifies each statement
If M is between X and Y, then XM+MY=XY
Segment Addition Postulate

4. Bellwork Solution
Find the measure of MN if N is between M and P and MP=6x-2, MN=4x, and MP=16. P N M

5. Use Postulates and Diagrams
Section 2.4

6. The Concept
Up until this point we’ve learned quite a few postulates and the basics of logic
Today we’re going to begin to put the two together

7. The Postulates The postulates that we’re using can be found on pg. 96
We’re going to briefly discuss them, however it is going to be up to you to find time to copy them out of the book and put them in your notes
The postulates we’ve seen
Postulate 1: Ruler Postulate
Postulate 2: Segment Addition Postulate
Postulate 3: Protractor Postulate
Postulate 4: Angle Addition Postulate
Axis of symmetry
Vertex

8. The Postulates The postulates we’ve used, but never named
Postulate 5: Through any two points there exists exactly one line
Postulate 6: A line contains at least two points
Postulate 7: If two lines intersect, then their intersection is exactly one point
Postulate 8: Through any three non-collinear points there exists exactly one plane
Postulate 9: A plane contains at least three non-collinear points
Postulate 10: If two points lie in a plane, then the line containing them lies in the plane
Postulate 11: If two planes intersect, then their intersection is a line
Axis of symmetry
Vertex

9. Why do we need these?
When we see something occur we can now reference it by way of theory
For example
State the postulate illustrated in the pictures
Axis of symmetry
Vertex

10. Example
Another use is to use the postulates as a blueprint for statements about a diagram
For example
Use this diagram to write examples of Postulate 6 & 8
Postulate 6:
If line l exists, then points R and S are on the line
Postulate 8:
If points W, R, S are non-collinear, then plane M exists

11. Perpendicular Figures
A line is a line perpendicular to a plane if and only if the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at the point
What?
Axis of symmetry
Vertex

12. Assumptions
When using postulates we have to be cognizant of the concern over assumed information
We can only use given information from a diagram
Assuming that properties based on “what looks good” is erroneous
Axis of symmetry
Vertex

13. Example Which of the following cannot be assumed from the diagram? r E
Axis of symmetry
Vertex

14. Homework
2.4
1-23, 30-34

15. Most Important Points Postulates 5-11 How to use postulates as a model
Using postulates to show what’s true and what’s not